Two concentric circular coils, C1 and C2, are placed in the XY plane. C1 has 500 turns, and a radius of 1 cm. C2 has 200 turns and radius of 20 cm. C2 carries a time dependent current I(t) = (5t2 – 2t + 3) A where t is in s. The emf induced in C1 (in mV), at the instant t 1s is \frac{4}{x} . The value of x is …….

Engineering

Physics

Magnet and Magnetic Dipole Moment

Question

Two concentric circular coils, C₁ and C₂, are placed in the XY plane. C₁ has 500 turns, and a radius of 1 cm. C₂ has 200 turns and radius of 20 cm. C₂ carries a time dependent current I(t) = (5t² – 2t + 3) A where t is in s. The emf induced in C₁ (in mV), at the instant t 1s is $\frac{4}{x}$ . The value of x is …….

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I = (5t² + 2t + C)

$\frac{di}{dt} = (10 t + 2)$

$ϕ_{small} = BA = (\frac{μ_{0} {IN}_{2}}{2 R}) ({πr}^{2})$

induced emf in small coil

$e = \frac{dϕ}{dt} = (\frac{μ_{0} N_{2}}{2 r}) {πr}^{2} N_{1} \frac{di}{dt} = (\frac{μ_{0} N_{1} N_{2} {πr}^{2}}{2 R}) (10 t - 2)$

at t = 1

$e = (\frac{μ_{0} N_{1} N_{2} {πr}^{2}}{2 R}) 8 = 4 \frac{μ_{0} N_{1} N_{2} {πr}^{2}}{R} = \frac{4 (4 π) 10^{- 7} \times 200}{20} \times 500 \times \frac{10^{- 4}}{10^{- 2}} π$

= 80 × p² × 10^–7 × 10 × 10² × 10^–2 = 8 × 10^–4 volt = 0.8 mV $= \frac{4}{x}$

x = 5.

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